Three-dimensional surface structure for reduced friction resistance and improved heat exchange

ABSTRACT

In order to improve the flow properties of a surface, a surface along which a medium flows is provided. The medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases and the surface comprises dimples, the edges of which are rounded, thereby forming a central dimple area and at least one curvature area for each dimple. The at least one curvature area continuously connects the dimple to the surrounding surface.

The invention concerns in general surfaces along which media, e.g.gases, liquids or two-phase mixtures are flowing and especially surfacesas described in EP 92 911 873.5, PCT RU92/00106 or EP 96 927 047.9,PCT/EP96/03200 also termed TLT-reliefs or TLT-surfaces.

It is known that the process when a continuous medium like a gas, aliquid or a two-phase mixture flows along a surface covered with veryspecial three-dimensional concave reliefs, named the TLT-reliefs andbeing described in more detail in EP 92 911 873.5, PCT RU92/00106 and inEP 96 927 047.9, PCT/EP96/03200, which are completely incorporated hereby reference, is accompanied by self-organization of secondary twistedtornado-like jets originating in each concavity of the relief andflowing out of it into the parent flow.

It is known that friction could be reduced by means of dimples locatedat said surface and that in addition heat transfer between said surfaceand the streaming media, e.g. gases, liquids and two-phase mixturescontaining gases and liquids could be increased.

However, there are special situations in which there is minor interestin drag reduction and major interest in an increased heat transfer, asfor instance for heat exchange devices as heat sinks in general,bonnets, chillers and many more. In addition, a huge number of devicesdemand for drag reduction as vehicles, aircrafts and ships in general.Moreover, any fluid transportation would benefit from a reduced dragresistance as this would decrease energy consumption or increasetransportation speed.

Therefore it is an object of the invention to show a new way how theproperties of a surface, especially concerning friction resistance andheat exchange with a surrounding medium, can be improved.

The object of the invention is achieved in a surprisingly simple mannerby a subject matter of one of the attached independent claims.Advantageous embodiments and refinements are defined in the respectivedependent claims.

The inventors surprisingly found that a certain geometry of theTLT-reliefs results in a significant improvement of the flow properties.

Accordingly the invention proposes a surface, which comprises dimples,wherein the edges of said dimples are rounded, thereby forming a centraldimple area and at least one curvature area for each dimple, whichcontinuously connects the dimple to the surrounding surface.

Such a geometry of a surface especially improves the flow propertieswith respect to friction resistance as also with respect to heat andmass transfer for surfaces, along which a medium flows, which consistsof a gas, a liquid, a two-phase mixture, or a mixture of multiplephases.

The underlying principle are secondary vortices, which originate in thedimples and lead to an organized transportation of medium from thesurface to the main flow. Due to the reduced pressure inside the vortexflows the boundary layer is sucked in, so that the thickness of theboundary layer does not increase.

Said central dimple preferably area essentially has the form of asection of a sphere or an ellipsoid.

With great advantage said curvature area of the surface comprises atleast a first curvature area and a second curvature area, the firstcurvature area having a different curvature than the second curvaturearea. Preferably said first curvature area is rounded with a firstrounding radius and said second curvature area is rounded with a secondrounding radius.

As will also be seen later on, especially suitable for drag reduction,i.e. reduction of friction resistance, and related flow properties likereduced drag vortices and reduced lee waves, is a surface comprisingdimples having a relatively low depth in relation to the diameter. Inthis regime it can be of special advantage to combine two different,consecutive curvature areas to realize different sizes of the centraldimple area.

Also two curvature areas are very advantageous in order to achieve agentle transition from the dimple to the surrounding surface, therebyreducing the probability of destruction of the advantageous secondaryvortices, which originate in the dimples.

With advantage the dimples are arranged periodically on the surface. Inorder to realize a good coverage of the surface, the centers of threeadjoining dimples preferably form a triangle, the distance between twoneighboring dimples having a constant value t₁ and the distance betweentwo rows of dimples having a constant value t₂.

The maximum coverage can be reached in this kind of arrangement when thecurvature areas of said three adjoining dimples are in contact with eachother.

Even in this arrangement a small area of flat surface remains in thecenter of three respective adjoining dimples. In this locationpreferably additional smaller-sized dimples are provided, by which theflow properties can be further improved.

The inventors also surprisingly found that there are regimes ofsignificantly increased heat exchange and regimes of strongly reduceddrag resistance.

Accordingly a surface, along which a medium flows, said mediumconsisting of a gas, a liquid, a two-phase mixture, or a mixture ofmultiple phases, with dimples having a diameter d and a depth h with aratio between said depth and said diameter of h/d≦0.1, also lies withinthe scope of the invention. In this geometrical regime the surface showsan especially low friction resistance.

With a ratio of h/d≧0.1 the surface shows an especially high heattransfer between said surface and said flowing medium.

The dimpled surfaces or reliefs with small relative depth of h/d≦0.1,where h is the concavity depth and d is the concavity diameter,significantly reduce the friction resistance of the shaped surfaces, aswell as intensify the heat and mass transfer, to a lesser extend,however, as compared with the friction resistance of a smooth surface.

The dimpled surfaces or reliefs with a larger relative depth of h/d≧0,1significantly intensify the heat and mass transfer with theaerohydrodynamic losses being constant or lagging behind the rate ofintensification, with considerable disturbance of Reynolds in favoriteto heat transfer.

Also within the scope of the invention lies a means for locomotion withat least one surface, along which a medium flows when said means forlocomotion is in movement, wherein the at least one surface is providedwith dimples as described above, in particular provided as a car, atruck, a train, an airplane, a helicopter or a ship.

In comparison to an otherwise identical means for locomotion or vehiclewith a flat surface certain flow properties are improved, especially thedrag resistance is reduced, the forming of drag vortices is reduced, theforming of lee waves is reduced, and the separation point of the flow ismoved further downstream.

Further a device for transportation of a medium lies within the scope ofthe invention, which comprises at least one surface with dimples asdescribed above. With advantage the surface with dimples is provided asan inner surface of a transport channel, in particular a pipe, of thedevice, in which the medium is transported. The implementation in such adevice is of advantage due to a further result of the described surfacestructure found by the inventors, consisting in a reduced deposition ofparticles on the surface compared to a flat surface.

Further a device for heat exchange between a flowing medium and at leastone surface of the device, in particular an air-conditioning system orpart thereof, is proposed, wherein the at least one surface is providedwith dimples. Here it can be taken advantage of the effect of reducedice-forming on a surface, which comprises the described dimples, incomparison to a flat surface.

The invention further proposes a container for cooking and/or forkeeping warm, wherein the outside surface of the bottom wall of thecontainer and/or the outside surface of the side walls of the containercomprise a surface with the described dimples.

Also a layer or coating for applying on a surface is proposed,which-comprises a surface with the described dimples. By use of such alayer, a device or vehicle having a surface along which a medium flowscan be upgraded for improved flow properties, such as reduced frictionresistance or improved heat or mass transfer or a combination thereof.

For this purpose the layer can advantageously be provided with a firstside and a second side, wherein said first side comprises dimples asdescribed above and said second side comprises a self-adhesive coating.

Accordingly the invention proposes a method for producing a surface withreduced friction resistance and/or improved heat exchange with asurrounding medium, comprising the step of applying a described layeronto said surface.

Also a method is proposed for producing a surface with reduced frictionresistance and/or improved heat exchange with a surrounding medium,which comprises the steps of

-   -   providing a workpiece with at least one surface and    -   imprinting into said at least one surface a structure comprising        dimples.

Another inventive method for producing a surface with reduced frictionresistance and/or improved heat exchange with a surrounding medium,comprises the steps of

-   -   providing a casting mold with at least one structured surface        and    -   molding, in particular injection molding, of a workpiece with at        least one surface comprising dimples by means of said casting        mold.

The invention is not limited to the described production methods, butshall also encompass any other method, which is suitable to produce asurface comprising the above described dimples.

Also within the scope of the invention lies the usage of a surface withdimples as described above as a surface of

-   -   a means for locomotion or    -   a device for transportation of a medium or    -   a device for heat exchange or    -   a container for cooking and/or for keeping warm.

In the following the invention is described exemplary in more detail onthe basis of preferred embodiments and with reference to the encloseddrawings. Therein same reference marks in the drawings indicate same orsimilar parts.

BRIEF DESCRIPTION OF THE FIGURES

It is shown in:

FIG. 1: a schematic diagram of a first distribution of dimples,

FIG. 2: a schematic diagram of a cross section through a dimpleaccording to a first preferred embodiment,

FIG. 1: a schematic diagram of a second distribution of dimples,

FIG. 4: a schematic diagram of a cross section through a dimpleaccording to a second preferred embodiment,

FIG. 5: a schematic diagram of a train with an inventive surface,

FIG. 6: schematically a comparison of two wing profiles,

FIG. 7: a schematic diagram of a container immersed in a flowing fluid,

FIG. 8: schematically a transport channel, the inner surface of whichbeing provided with dimples,

FIG. 9: a schematic diagram of a measurement arrangement for measuringthe velocity profiles over different investigated plates comprising alaser Doppler anemometer (LDA),

FIG. 10: a schematic diagram of a metal plate with TLT relieves ordimples,

FIG. 11: a schematic diagram of a plate with variable TLT relieves ordimples,

FIG. 12: a schematic diagram of a plate with TLT relieves showing thepoints, at which the velocity was measured.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows schematically a preferred distribution of dimples 10 on asurface. The dimples 10 are arranged periodically, wherein the centersof three directly adjoining dimples 10 form an equilateral triangle. Theangle α therefore has a value of 60°. The distance between the centersof two adjoining dimples 10, which is equal to the length of a side ofthe triangle, has a constant value t₁. The distance between two rows ofdimples 10, which equals the height of the triangle, has a constantvalue t₂. The parameters t₁ and t₂ can have different values dependingon the purpose for which the surface shall be utilized.

FIG. 2 shows a cross section through the center of one of the dimples 10shown in FIG. 1, perpendicular to the surface. In this embodiment thedimple essentially has the form of a calotte with radius R_(ahp), heighth_(c) and diameter d_(c). Further the dimple 10 is rounded at the edgeswith a rounding radius R_(S). Thereby in this example the dimple issymmetrical with respect to rotation around an axis through the centerof the dimple and perpendicular to the surface.

FIG. 3 shows schematically a top view of a distribution of dimplescomprising a central dimple area 110, a first curvature area 120 and asecond curvature area 130, the named areas being arranged consecutivelyfrom the center of the dimple to the outside.

The central dimple area has a diameter of d₁, the first curvature areahas an diameter of d₂ and the second curvature area has a diameter oft₁. The dimples are arranged similar to FIG. 1, but in this preferredembodiment the outer rims of two adjoining dimples are in contact witheach other for a maximum surface coverage.

Again, the centers of three adjoining dimples form an equilateraltriangle, the distance between the centers of two adjoining dimpleshaving the constant value t₁ and the distance between two rows ofdimples having the constant value t₂. In this embodiment therefore thediameter of the second curvature area equals the distance between twoadjoining dimples t₁.

A small area of surface remains in the center between three adjoiningdimples. In this location preferably additional smaller-sized dimples200 can be provided, thereby further improving the flow properties ofthe surface.

The cross section AA′ through the center of a dimple perpendicular tothe surface is shown in more detail in FIG. 4.

The central dimple area 110 essentially has the form of a section of asphere, followed in the outward direction by two consecutive curvatureareas. Since the curvature areas can be described as an arc, which isrotated in space, they have a surface formed as a part of a torus orsimilar thereto.

The form of the central dimple area, of the first curvature area and ofthe second curvature area in the shown cross section perpendicular tothe surface and through the center of the dimple is defined by thefollowing parameters:

-   d₁: Diameter of the central dimple area,-   d₂: Outer diameter of the first curvature area,-   t₁: Outer diameter of the second curvature area,-   R₁, C₁: Radius and center point of the sphere, the section of which    forms the surface of the central dimple area,-   R₂, C₂: Radius and center point of the rounding radius of the first    curvature area,-   R₃, C₃: Radius and center point of the rounding radius of the second    curvature area,-   P₁: Transition point from the central dimple area to the first    curvature area,-   P₂: Transition point from the first curvature area to the second    curvature area,-   P₃: Transition point from the second curvature area to the    surrounding surface,-   h₁: Difference in height between the lowest point of the central    dimple area and the outer rim of the central dimple area,-   h₂: Difference in height between the inner rim of the first    curvature area and the outer rim of the first curvature area,-   h₃: Difference in height between the inner rim of the second    curvature area and the outer rim of the second curvature area,-   α₁: Angle between the y-axis and a line connecting C₂ and C₃,-   α₂: Angle between the x-axis and a line connecting C₁ and C₂,-   f: Parameter related to the portion of the surface covered by the    central dimple area in relation to the combined area of central    dimple area and curvature areas.

There is one point, in which the circle with radius R₁, being part ofthe sphere that forms the central dimple area, and the circle withradius R₂, defining the curvature of the first curvature area, have amutual tangent. Further, there is another point, in which the circlewith radius R₂ and the circle with radius R₃ have a mutual tangent.

To completely describe the form of the dimple a set of parameters, inparticular the parameters d₁, α₁, α₂, R₂/R₁ and f, are chosen accordingto the necessities of the specific purpose the surface shall be used forand depending on whether drag reduction or improved heat exchange haspriority. For most purposes the coverage of the surface by the centraldimple areas lies below 70%, but also a greater coverage falls withinthe scope of the present invention.

The remaining of the named parameters can be calculated by means of thefollowing equations:${R_{1} = \frac{d_{1}}{{2 \cdot \sin}\quad\alpha_{1}}},{R_{2} = {\frac{R_{2}}{R_{1}} \cdot \frac{d_{1}}{{2 \cdot \sin}\quad\alpha_{1}}}},{R_{2} = \frac{t_{1} - {\frac{d_{1}}{2} \cdot \frac{R_{2}}{R_{1}} \cdot \frac{\left( {1 - {\sin\quad\alpha_{1}}} \right)}{\sin\quad\alpha_{2}}}}{\sin\quad\alpha_{2}}},{h_{1} = {\frac{d_{1}}{2} \cdot \frac{\left( {1 - {\cos\quad\alpha_{1}}} \right)}{\sin\quad\alpha_{1}}}},{h_{2} = {R_{2} \cdot \left( {{\cos\quad\alpha_{2}} - {\cos\quad\alpha_{1}}} \right)}},{h_{3} = {R_{3} \cdot \left( {1 - {\cos\quad\alpha_{2}}} \right)}},{H = {h_{1} + h_{2} + h_{3}}},{t_{1} = {\sqrt{\frac{\pi}{6 \cdot f}} \cdot d_{1}}},{C_{1} = {{\left( {X_{C\quad 1},Y_{C\quad 1}} \right)\quad{with}\quad X_{C\quad 1}} = 0}},{Y_{C\quad 1} = {R_{1} - H}},{C_{2} = {{\left( {X_{C\quad 2},Y_{C\quad 2}} \right)\quad{with}\quad X_{C\quad 2}} = {\frac{d_{1}}{2} \cdot \left( {1 + \frac{R_{2}}{R_{1}}} \right)}}},{Y_{C\quad 2} = {R_{3} + \frac{X_{C\quad 3} - X_{C\quad 2}}{{tg}\quad\alpha_{2}}}},{C_{3} = {{\left( {X_{C\quad 3},Y_{C\quad 3}} \right)\quad{with}\quad X_{C\quad 3}} = \frac{t_{1}}{2}}},{Y_{C\quad 3} = {- R_{3}}},{P_{1} = {{\left( {X_{P\quad 1},Y_{P\quad 1}} \right)\quad{with}\quad X_{P\quad 1}} = \frac{d_{1}}{2}}},{Y_{P\quad 1} = {H - h_{1}}},{P_{2} = {{\left( {X_{P\quad 2},Y_{P\quad 2}} \right)\quad{with}\quad X_{P\quad 2}} = {\frac{t_{1}}{2} - {{R_{3} \cdot \sin}\quad\alpha_{2}}}}},{Y_{P\quad 2} = {R_{3} \cdot \left( {{\cos\quad\alpha_{2}} - 1} \right)}},{P_{3} = {{\left( {X_{P\quad 3},Y_{P\quad 3}} \right)\quad{with}\quad X_{P\quad 3}} = \frac{t_{1}}{2}}},{Y_{P\quad 3} = 0},$said equations being defined in a two-dimensional coordinate-system withthe x-axis in the plane of the surface and with the y-axis through thecenter of the dimple and perpendicular to the surface.

In FIGS. 5 to 8 various preferred embodiments of the invention areshown, thereby demonstrating the broad range of applications, for whichan inventive surface with dimples as described above can be utilized.The shown embodiments are only exemplary and do not limit the scope ofthe invention, as numerous other applications could be named.

In FIG. 5 a high-speed train 300 is shown schematically, which isprovided with an inventive outer surface 310, which comprises amultitude of dimples, the form, size and distribution of which isadapted according to speed and geometry of the train 300.

A train as shown in FIG. 5 is characterized by improved flow propertiesin comparison to a similar train with a flat surface. In particular theforming of drag vortices is reduced as also the forming of lee wave incase of side winds. Consequently the overall friction resistance is alsoreduced.

A further effect of the inventive surface lies in the separation pointof the flow being moved further downstream or in certain circumstancesthe complete disappearance of a separation point. This effect allows forinstance for providing completely new wing profiles. In FIG. 6 aconventional wing profile 400 is shown in comparison with a modifiedwing profile 410, the use of which becomes possible for example as awing of an airplane, when the surface is provided with an inventivedimple structure.

FIG. 7 shows a further utilization of an inventive surface for acontainer usable for cooking or for keeping some substance at a desiredtemperature. The container schematically shown in FIG. 7 is immersed ina flowing fluid 510. The outside surface of the bottom wall 520 of thecontainer and/or the outside surface of the side walls 530 of thecontainer comprise a surface with periodically arranged dimples.

In this embodiment the dimples are of the type shown in FIG. 1 and FIG.2, preferably with the following values:

-   t₁=28.6 mm,-   t₂=33.0 mm,-   d_(c)=20.0 mm,-   h_(c)=3.0 mm,-   R_(ahp)=68.2 mm,-   R_(S)=5.0 mm,    or scaled up or down keeping essentially the ratios    ${\frac{t_{1}}{t_{2}} = \frac{28.6}{33.0}},{\frac{R_{ahp}}{R_{S}} = \frac{68.2}{3.0}},{\frac{R_{S}}{h_{c}} = \frac{5.0}{3.0}}$

The above named values result in a fraction of the surface, which iscovered by the dimples, of about 0.3.

FIG. 8 schematically shows a pipe 600, the inner surface 610 of which isprovided with dimples 630. This pipe can be utilized as a transportchannel for transportation of a medium. The significant improvementachieved by using the inventive surface in this embodiment lies in areduced deposition of particles on the surface due to the suction of theboundary layer from the surface into the main flow by means of theself-organizing vortex flows originating in the dimples.

Furthermore, because of the same reasons the forming of ice on thesurface is reduced, so that such a pipe can also be utilized with greatadvantage in a device, in which a medium is to be cooled, like anair-conditioning system, especially an air-conditioning system used inan airplane.

The inventors have studied the phenomenon of friction resistancereduction on the TLT-relief surfaces using a laser Doppler anemometer(LDA) to measure velocity profiles formed over the surfaces being flowedaround, and the theorem of momentum to process the obtained results. Theexperimental setup is schematically illustrated in FIG. 9.

The investigated plate 704 is positioned in the test section 710 of thecavitation tunnel. By means of a laser 706 arranged on an optical bench708 and a signal control and preliminary processing unit 702 as parts ofthe laser Doppler anemometer (LDA) the flow properties are measured.

The test specimens, which were examined by the inventors, were thin flatplates of the following two types:

-   metal plates 800 of size 378×679 mm² either having a smooth surface    or a TLT-relief formed surface provided with dimples 802 as shown in    FIG. 10,-   plates 810 of the same size with an elastic rubber coating 820    applied onto a flat plate with either a continuous surface or a    surface provided with the regular grid of axially symmetrical holes    connecting the elastic coating 820 above them with the    pressure-tight chamber beneath the plate 810 as shown in FIG. 11.

By varying the pressure in the pressure-tight chamber, theexperimentalist can form on the flowed-around surface the TLT reliefwith various depth of the concavities by retracting the elastic coating820 inside the hole in the plate. When the pressure above and beneaththe plate is the same, the surface being flowed around represents a gridof rubber membranes covering the holes in the plate and interacting withthe ambient flow. Reducing the pressure beneath the plate, one cancontrol the TLT relief with the depth of the relief concavities varyingalmost from zero to the depths corresponding to the radius of the holein the support plate.

FIG. 11 further shows bearing cylinders 830, the vacuum cover 850, whichseals the air-tight chamber and a vacuum union 840.

A similar arrangement as the one shown in FIG. 11 can also be used in adevice or a vehicle to change the size, the form and/or the number ofthe dimples on the surface during operation of said device or vehicle.That way the flow properties of the device or vehicle can be flexiblyadapted to changing operating conditions.

During the experiment performed by the inventors the hydrodynamiccharacteristics of the following objects were compared:

-   -   the TLT-relief metal plate with the smooth surface metal plate;    -   the adjustable elastic TLT-relief plate with the smooth plate        with no holes on the support plate having the same elastic        coating;    -   the plates with various TLT reliefs on the metal surface with        the plates with membranes and different TLT reliefs on the        elastic surface.

The measurements were carried out in a cavitational tunnel, which wasthe cavitational tunnel of the Hamburgische Schiffbau-VersuchsanstaltGmbH (HSVA), in which the flow was characterized by the Reynolds numbersdefined as follows:

-   -   along the plate length considering the preliminary section        within the range:        9×10⁵ ≦Re≦7,5×10⁶;    -   along the TLT relief concavity diameter within the range:        2.5×10⁴ ≦Re≦6×10⁵.        The onflowing stream turbulence rate was high and according to        the laser measurements comprised:        0.1≦σ≈√(u′²)/u∞≦0.3

The water temperature in the flow was measured within the range:15° C.≦T≦ 22° C.The velocity profiles were measured at thirty points 930 arranged on thesurface of the plate 910 shown in FIG. 12. The profile speedmeasurements on the ambient surfaces of the flat plates and the plateswith TLT relief comprising dimples 920 were performed at these points930, which are indicated by crosses.

The measurements were processed using the theorem of momentum inaccordance with the procedure suggested by I.Nikuradze in “TurbulenteReibungsschichten an der Platte”, ZWB, R.Oldenbourg, Muenchen undBerlin, 1942, and comprised determination of the values of the local andfull friction resistance coefficients C′ and C_(F). The experimentaldata are represented in the table shown below.

It follows from the table that the friction resistance of the metallicsurface with the TLT relief is ˜22% lower than that of the smoothmetallic surfaces. The friction resistance of the surface with elasticrough rubber coating and the TLT relief on it is ˜34% lower than that ofthe smooth elastic rough rubber coated surface.

1. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising: dimples, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.
 2. The surface according to claim 1, wherein said central dimple area essentially has the form of a section of a sphere or an ellipsoid.
 3. (canceled)
 4. The surface according to claim 1, wherein said first curvature area is rounded with a first rounding radius and said second curvature area is rounded with a second rounding radius.
 5. The surface according to claim 4, wherein said central dimple area essentially has the form of a section of a sphere, and the form of the central dimple area, of the first curvature area and of the second curvature area in a cross section perpendicular to said surrounding surface and through a center of the dimple is defined by the following parameters: d₁: Diameter of the central dimple area, d₂: Outer diameter of the first curvature area, t₁: Outer diameter of the second curvature area, R₁, C₁: Radius and center point of the sphere, the section of which forms the surface of the central dimple area, R₂, C₂: Radius and center point of the rounding radius of the first curvature area, R₃, C₃: Radius and center point of the rounding radius of the second curvature area, P₁: Transition point from the central dimple area to the first curvature area, P₂: Transition point from the first curvature area to the second curvature area, P₃: Transition point from the second curvature area to the surrounding surface, h₁: Difference in height between the lowest point of the central dimple area and the outer rim of the central dimple area, h₂: Difference in height between the inner rim of the first curvature area and the outer rim of the first curvature area, h₃: Difference in height between the inner rim of the second curvature area and the outer rim of the second curvature area, α₁: Angle between the y-axis and a line connecting C₂ and C₃, α₂: Angle between the x-axis and a line connecting C₁ and C₂, f: Parameter related to the portion of the surface covered by the central dimple area in relation to the combined area of central dimple area and curvature areas, wherein a set of parameters, in particular the parameters comprising d₁, α₁, α₂, R₂/R₁ and f, are chosen and a remaining set of parameters are calculated by the following equations with a tolerance of ±10% for each parameter: ${R_{1} = \frac{d_{1}}{{2 \cdot \sin}\quad\alpha_{1}}},{R_{2} = {\frac{R_{2}}{R_{1}} \cdot \frac{d_{1}}{{2 \cdot \sin}\quad\alpha_{1}}}},{R_{2} = \frac{t_{1} - {\frac{d_{1}}{2} \cdot \frac{R_{2}}{R_{1}} \cdot \frac{\left( {1 - {\sin\quad\alpha_{1}}} \right)}{\sin\quad\alpha_{2}}}}{\sin\quad\alpha_{2}}},{h_{1} = {\frac{d_{1}}{2} \cdot \frac{\left( {1 - {\cos\quad\alpha_{1}}} \right)}{\sin\quad\alpha_{1}}}},{h_{2} = {R_{2} \cdot \left( {{\cos\quad\alpha_{2}} - {\cos\quad\alpha_{1}}} \right)}},{h_{3} = {R_{3} \cdot \left( {1 - {\cos\quad\alpha_{2}}} \right)}},{H = {h_{1} + h_{2} + h_{3}}},{t_{1} = {\sqrt{\frac{\pi}{6 \cdot f}} \cdot d_{1}}},{C_{1} = {{\left( {X_{C\quad 1},Y_{C\quad 1}} \right)\quad{with}\quad X_{C\quad 1}} = 0}},{Y_{C\quad 1} = {R_{1} - H}},{C_{2} = {{\left( {X_{C\quad 2},Y_{C\quad 2}} \right)\quad{with}\quad X_{C\quad 2}} = {\frac{d_{1}}{2} \cdot \left( {1 + \frac{R_{2}}{R_{1}}} \right)}}},{Y_{C\quad 2} = {R_{3} + \frac{X_{C\quad 3} - X_{C\quad 2}}{{tg}\quad\alpha_{2}}}},{C_{3} = {{\left( {X_{C\quad 3},Y_{C\quad 3}} \right)\quad{with}\quad X_{C\quad 3}} = \frac{t_{1}}{2}}},{Y_{C\quad 3} = {- R_{3}}},{P_{1} = {{\left( {X_{P\quad 1},Y_{P\quad 1}} \right)\quad{with}\quad X_{P\quad 1}} = \frac{d_{1}}{2}}},{Y_{P\quad 1} = {H - h_{1}}},{P_{2} = {{\left( {X_{P\quad 2},Y_{P\quad 2}} \right)\quad{with}\quad X_{P\quad 2}} = {\frac{t_{1}}{2} - {{R_{3} \cdot \sin}\quad\alpha_{2}}}}},{Y_{P\quad 2} = {R_{3} \cdot \left( {{\cos\quad\alpha_{2}} - 1} \right)}},{P_{3} = {{\left( {X_{P\quad 3},Y_{P\quad 3}} \right)\quad{with}\quad X_{P\quad 3}} = \frac{t_{1}}{2}}},{Y_{P\quad 3} = 0},$ said equations being defined in a two-dimensional coordinate-system with an x-axis in the plane of said surrounding surface and with the a y-axis through the center of the dimple and perpendicular to said surrounding surface.
 6. The surface according to claim 1, wherein said dimples are arranged periodically on said surrounding surface.
 7. The surface according to claim 5, wherein the centers of three adjoining dimples form a triangle, a first distance between two neighboring dimples of said triangle having a constant value t₁, and a second distance between two rows of the dimples having a constant value t₂.
 8. The surface according to claim 7, wherein the at least one curvature areas of said three adjoining dimples are in contact with each other.
 9. The surface according to claim 7, further comprising additional dimples of a different size than said dimples, which are located in the center of three respective adjoining dimples.
 10. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, comprising: dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d less than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface.
 11. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising: dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d greater than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface. 12 and
 13. (canceled).
 14. The surface according to claim 1, wherein said surrounding surface comprises a locomotive device selected from the group consisting of a car, a truck, a train, an airplane, a helicopter and a ship. 15 and
 16. (canceled).
 17. The surface according to claim 1, wherein said surrounding surface comprises an inner surface of a transport channel.
 18. The surface according to claim 17, wherein said transport channel is a pipe.
 19. (canceled)
 20. The surface according to claim 1, wherein said surrounding surface comprises a device for heat exchange between a the medium and at least one surface of the device.
 21. (canceled)
 22. The surface according to claim 1, wherein said surrounding surface comprises a container for cooking and/or for keeping warm, said surrounding surface being located at an outside surface of a bottom wall of the container and/or an outside surface of side walls of the container.
 23. A layer for applying on a surface, comprising: a surface with dimples wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, and wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.
 24. The layer according to claim 23, further comprising a first side and a second side, wherein said first side comprises said surface and said second side is self-adhesive.
 25. A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the step of: forming a layer having a first side with dimples and a second side with an adhesive, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area; and applying a said second side of said layer onto said surface.
 26. The method according to claim 25, further comprising the steps of: imprinting said dimples into said first side.
 27. A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the steps of: providing a casting mold with at least one structured surface; and molding a workpiece with at least one surface in contact with said at least one structured surface to define comprising dimples, on the workpiece, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.
 28. (canceled) 